Encouraging second-order consistency for multiple graph matching

Park, Han-Mu; Yoon, Kuk-Jin

doi:10.1007/s00138-016-0786-2

Cited by 3 publications

(4 citation statements)

References 28 publications

(78 reference statements)

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“…The vertex-aligned graphs are common in many applications of interest such as neuroimaging [22], multilayer networks [23] or time-varying graphs [7]. In case that the graphs are not aligned, graph matching should be performed before the joint embedding [24], [25]. The mis-alignments of some vertices will have adverse effects in estimating corresponding latent positions in H; however, a small number of mis-aligned vertices should not have a big impact in estimating Λ.…”

Section: Joint Embedding Of Graphsmentioning

confidence: 99%

Joint Embedding of Graphs

Wang

Arroyo

Vogelstein

et al. 2021

IEEE Trans. Pattern Anal. Mach. Intell.

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Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a method to jointly embed multiple undirected graphs. Given a set of graphs, the joint embedding method identifies a linear subspace spanned by rank one symmetric matrices and projects adjacency matrices of graphs into this subspace. The projection coefficients can be treated as features of the graphs, while the embedding components can represent vertex features. We also propose a random graph model for multiple graphs that generalizes other classical models for graphs. We show through theory and numerical experiments that under the model, the joint embedding method produces estimates of parameters with small errors. Via simulation experiments, we demonstrate that the joint embedding method produces features which lead to state of the art performance in classifying graphs. Applying the joint embedding method to human brain graphs, we find it extracts interpretable features with good prediction accuracy in different tasks.

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Section: Joint Embedding Of Graphsmentioning

confidence: 99%

Joint Embedding of Graphs

Wang

Arroyo

Vogelstein

et al. 2021

IEEE Trans. Pattern Anal. Mach. Intell.

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“…Pair-wise algorithms search for matches between two graphs, whereas multi-graph algorithms try to find a consistent mapping across a set of graphs. Many of these algorithms act more like frameworks that can incorporate pair-wise matching algorithms, such as [27][28][29][30]. In our research material, only two examples of each process plant type were available, so only pair-wise graph matching algorithms were used.…”

Section: Graph Matchingmentioning

confidence: 99%

Applying graph matching techniques to enhance reuse of plant design information

Rantala¹,

Niemistö²,

Karhela

et al. 2019

Computers in Industry

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This article investigates how graph matching can be applied to process plant design data in order to support the reuse of previous designs. A literature review of existing graph matching algorithms is performed, and a group of algorithms is chosen for further testing. A use case from early phase plant design is presented. A methodology for addressing the use case is proposed, including graph simplification algorithms and node similarity measures, so that existing graph matching algorithms can be applied in the process plant domain. The proposed methodology is evaluated empirically on an industrial case consisting of design data from several pulp and paper plants.

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“…The multiple graph matching problem can be formulated as a summation of individual pairwise matching problems as follows [13,17]:…”

Section: Multiple Graph Matching Problems With Multiple Attributesmentioning

confidence: 99%

“…Yan et al [15,16] also proposed a flexible algorithm that gradually improves consistency over iteration. Park and Yoon [17] proposed an iterative framework that encourages the soft constraint based on the second-order consistency instead of enforcing the hard constraint of the cycle-consistency. Since this approach sequentially updates solutions from one graph pair to others, the final results are sensitive to the update sequence, and this often causes the error accumulation.…”

Section: Introductionmentioning

confidence: 99%

Consistent multiple graph matching with multi-layer random walks synchronization

Park

Yoon

2019

Pattern Recognition Letters

Self Cite

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We address the correspondence search problem among multiple graphs with complex properties while considering the matching consistency. We describe each pair of graphs by combining multiple attributes, then jointly match them in a unified framework. The main contribution of this paper is twofold. First, we formulate the global correspondence search problem of multi-attributed graphs by utilizing a set of multi-layer structures. The proposed formulation describes each pair of graphs as a multi-layer structure, and jointly considers whole matching pairs. Second, we propose a robust multiple graph matching method based on the multi-layer random walks framework. The proposed framework synchronizes movements of random walkers, and leads them to consistent matching candidates. In our extensive experiments, the proposed method exhibits robust and accurate performance over the state-of-the-art multiple graph matching algorithms.

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Encouraging second-order consistency for multiple graph matching

Cited by 3 publications

References 28 publications

Joint Embedding of Graphs

Joint Embedding of Graphs

Applying graph matching techniques to enhance reuse of plant design information

Consistent multiple graph matching with multi-layer random walks synchronization

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